Partial mirror symmetry, lattice presentations and algebraic monoids

Brent Everitt; John Fountain

doi:10.1112/plms/pds068

Partial mirror symmetry, lattice presentations and algebraic monoids

Brent Everitt, John Fountain

Mathematics

Research output: Contribution to journal › Article

Abstract

This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in Everitt and Fountain [Adv. Math. 223 (2010) 1782–1814]. In this paper, we study their presentations as abstract monoids. Along the way, we also find general presentations for certain join-semilattices (as monoids under join), which we interpret for two special classes of examples: the face lattices of convex polytopes and the geometric lattices, particularly the intersection lattices of hyperplane arrangements. Another spin-off is a general presentation for the Renner monoid of an algebraic monoid, which we illustrate in the special case of the ‘classical’ algebraic monoids.

Original language	English
Pages (from-to)	414-450
Number of pages	37
Journal	Proceedings of the London Mathematical Society
Volume	107
Issue number	2
Early online date	5 Feb 2013
DOIs	https://doi.org/10.1112/plms/pds068
Publication status	Published - 2 Aug 2013

Bibliographical note

(c) 2013 London Mathematical Society. his is an author produced version of a paper published in Proceedings of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.

Keywords

Algebra

Access to Document

10.1112/plms/pds068

refmonoids.final
(c) 2013 London Mathematical Society. his is an author produced version of a paper published in Proceedings of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.
Accepted author manuscript, 540 KB

http://plms.oxfordjournals.org/content/107/2/414

Cite this

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